PR #7070 changed gate equality comparison results

[mhucka]

Describe the issue

Users report that

cirq.X**0.5 == cirq.PhasedXPowGate(exponent=0.5, phase_exponent=0)

is True before the change and False afterwards. This is affecting internal code that uses this.

The fact that this difference was not picked up in CI checks probably means the test cases currently in Cirq need to be expanded to cover this.

[dstrain115]

FYI, the tests in #7070 were actually specifically changed so that this equality is tested differently:
https://github.com/quantumlib/Cirq/pull/7070/files#diff-6f870e177744f7a85e0f63617b263a531f4ac339b1a6c8976696326edd3f949aL82

[daxfohl]

With the flurry of these, I went through my PRs and labeled everything that could possibly be considered breaking, and added a comment to each summarizing the change: https://github.com/pulls?q=repo%3Aquantumlib%2FCirq+author%3Adaxfohl+merged%3A%3E2024+label%3A%22BREAKING+CHANGE%22. I think everything is benign but LMK if there's anything that needs further discussion.

[codrut3]

Let me know if I can help here.

[pavoljuhas]

The thing is we had a special case for the PhasedXPowGate equality which would make it masquerade as X or Y gates for their respective phase_exponent-s. With a hindsight, this was not the best choice and was a root cause for incorrect approximate comparisons in #6528. It was contrary to behavior of standard Python types, e.g., [], () and set() are all empty collections, but they test unequal to each other. The prior equality behavior is also inconsistent across cirq gates, for example cirq.I, cirq.X ** 0 evaluate as unequal even if both act as the identity operation.

My preference would be to consider #7070 a bug fix and the affected downstream code as case of code relying on a bug. The breakage of internal code this issue reports is easy to fix in a way that works for both pre and post #7070 code; I will submit a fix there shortly.

Hopefully, there is no other significant dependence that would compel us to revert #7070.